Question

2+(5)/(3k-6)=(-2)/(3k-6)^2

Answer 1

\[k \approx2.299, -1.823\]

Answer 2

They have to be fractions :[

Answer 3

k≈2.299,−1.823

Answer 4

Since we know that we are dealing with fractions, there are a couple ways to solve this:
1) Cross multiply.
2) Find a common denominator.
3) Multiply both sides with the variable with the biggest degree in the denominator to get rid of the fraction

I find it easiest to eliminate the fraction since we are dealing with the same (3k-6) on one side but (3k-6)^2 on the other, meaning (3k-6) (3k-6). So let's go through this question using that method. Whichever one works best for you might be different.

2+(5)/(3k-6)=(-2)/(3k-6)^2

In this case, (3k-6)^2 would be the factor we multiply both sides with.

(3k-6)^2 [2+(5)/(3k-6)] = (3k-6)^2 [(-2)/(3k-6)^2]

Cancel out some of the fractions to simplify things a bit.

(3k-6) (2+(5)) = (-2)
(3k-6) (7) = (-2)
(21k- 42) = (-2)
21k = (-2) + (42)
21k = (40)
k = 40/21